We investigate the rapid and anisotropic UV-induced photoconductive response of hybrid thin films comprising zinc oxide (ZnO) nanowires (NWs) directly grown on horizontally aligned (HA-) carbon nanotube (CNT) sheets. The films exhibit anisotropic photoconductivity; along the CNTs, conductivity is dominated by the CNTs and the photoconductive gain is lower, whereas perpendicular to the CNTs the photoconductive gain is higher because transport is influenced by ZnO nanoclusters bridging CNT-CNT contacts. Because of the distributed electrical contact provided by the large number of ZnO NWs on top of the HACNT film, this hybrid nanoarchitecture has a significantly greater photocurrent than reported for single ZnO NW-based devices at comparable UV illumination intensity. Moreover, the hybrid architecture where a thin basal film of ZnO ohmically contacts metallic CNTs enables rapid transport of photogenerated electrons from ZnO to CNTs, resulting in sub-second photoresponse upon pulsed illumination. The built-in potential generated across ZnO-CNT heterojunctions competes with the externally applied bias to control the photocurrent amplitude and direction. By tuning the anisotropic conductivity of the CNT network and the morphology of the ZnO or potentially other nanostructured coatings, this material architecture may be engineered in the future to realize high-performance optical and chemical sensors.